Q&A for How to Use a Number Line

Start at +209, then move 159 to the left.

Start at +6, then move 2 to the right.

Here's a very simple example of how to do that: Let's say we're dividing 2 into 6. Begin with the section of the number line from zero to 6. Count two units from zero to 2. Count another two units from 2 to 4. Count another two units from 4 to 6. So we have found that a length of two units exactly fits inside the length of six units three times. Thus, 2 divides into 6 three times.

A number line does not include units (such as km). However, you can choose to show divisions between integers if you choose to. 4.5 would simply be the point midway between 4 and 5 on the line.

Set up a number line calibrated in sixths. Then start at 1 3/6, or 9/6. To subtract a positive number, move to the left. Count 5/6 to the left. You'll end up at 4/6.

Divide the interval between zero and +1 into five equal segments. Each segment would represent 1/5. 3/5 is 3/5 of the way from zero to +1.

Start at zero. Move 4 units to the right. Move 5 more units to the right. Then move 6 units to the left. You'll finish at 3 units to the right of zero.

Use Method 3 above.

15/7 is 2 1/7. On a number line it lies 1/7 of the way from 2 to 3. If you divide the space between 2 and 3 into seven equal segments, 15/7 lies one segment to the right of 2.

To be absolutely accurate, you would have to divide each full number of the number line into 120 divisions (because 120 is the lowest common denominator of the three fractions). Then -20/3 would be -800/120, -5/8 would be - 75/120, and 7/5 would be 168/120. If you don't need to be that accurate, you could just estimate the places where those three numbers stand on the number line.

When adding a positive number on a number line, you move to the right. When adding a negative number, you move to the left. So in the case of 8 + (-3), you start by moving 8 units to the right of 0. That takes you to +8. Then you move 3 units to the left of +8, which takes you to +5. So the sum is +5, or simply 5.

7 is 7 units to the right of zero. 3 is 3 units to the right of zero. -5 is 5 units to the left of zero.

It doesn't matter how many digits are involved. The process remains the same. In this case, you start at 40 on the number line, then move 16 units to the right, then move 20 more units to the right. You wind up at 76 units to the right of zero.